一种求解约束非线性方程组的非精确Levenberg-Marquardt算法

An Inexact Levenberg-Marquardt Method for Solving Constrained Nonlinear Equations

利用绝对值函数的光滑函数将约束非线性方程组转化为一个光滑方程组,用非精确Levenberg-Mar-quardt方法求解该光滑方程组,得到一种求解约束非线性方程组的非精确Levenberg-Marquardt算法,证明该算法具有全局收敛性,并给出数值实验.

In this paper,we first transform the constrained nonlinear equations to a system of smooth equa-tions by using the smoothing approximation function of absolute value function. Then an inexact Levenberg-Marquardt method is used to solve the system of smooth equations,and get an inexact Levenberg-Marquardtalgorithm to solve constrained nonlinear equations,and the global convergence is obtained. Preliminary nu-merical results are given.